Supercyclic composition \(C_0\)-semigroups. (English) Zbl 07687030
Summary: In this paper, we extend the study of the supercyclicity of composition operators on \(H^2(\mathbb{D})\) and \(H^p(\mathbb{D})\) to \(C_0\)-semigroups and give some sufficient and necessary conditions (on the corresponding semiflow) for such a semigroup to be supercyclic. Finally, we show that supercyclic composition \(C_0\)-semigroups cannot exist on the Hardy spaces of the right half plane.
MSC:
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 47B33 | Linear composition operators |
Keywords:
semiflows; supercyclic composition \(C_0\)-semigroups; infinitesimal generators of semiflowsReferences:
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